This surface is called hyperbolic-paraboloid, made my yours truely Xah Toll. It is a surface made entirely of (straight) lines.
From this close up, one can see how this surface is curved, yet straight!

It is called hyperbolic-paraboloid because the horizontal cross sections are
hyperbolas
and diagonal vertical cross-sections are
parabolas.
This structure is commonly used as roofs for modern
pavillions.

You can easily make a hyperbolic-paraboloid. Imagine a cube. Mark
the top two opposite corners. These two corners will be the top two
vertexes of the surface you see in the above image. Now, also mark
the two opposite corners at the bottom of the cube. Draw diagonal
lines from these corners. (look at the figure above. Your diagonal
lines will be the edges of the surface) Mark regular intervals on these
diagonal lines. Now, connect lines from one diagonal to the other
side. You are all done!